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cornu spiral, spiros, clothoids, or Cornu spirals 回旋曲线

fresnelC(x), fresnelS(x)

An Euler spiral is a curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the radius). Euler spirals are also commonly referred to as spiros, clothoids, or Cornu spirals.

The spiral of Cornu appears in the study of diffraction in optics.

The curve is parametrically defined by the Fresnel cosine and sine integrals:

\[ \left[ ~ \int_0^x \cos \left( \frac{\pi}{2} t^2 \right) dt ~ , \int_0^x \cos \left( \frac{\pi}{2} t^2 \right) dt \right] ~ \]

Load its equations. Its animation can be done by click the checkbox.

Complete code for this example:



 

Examples Page - important curves